It is surprising (buttrue) that if 23 people are in the same room, there is about a 50%chance that at least two people will have the same birthday.Suppose you want to estimate the probability that if 30 people arein the same room, at least two of them will have the same birthday.You can proceed as follows.

a.Generate random birthdays for 30 different people. Ignoring thepossibility of a leap year, each person has a 1/365 chance ofhaving a given birthday (label the days of the year 1 to 365). Youcan use the RANDBETWEEN function to generate birthdays. What do youexpect the average birthday (a number between 1 and 365) among the30 people be?

b.Once you have generated 30 people's birthdays, how can you tellwhether at least two people have the same birthday? One way is touse Excel's RANK function. (You can learn how to use this functionin Excel's online help.) This function returns the rank of a numberrelative to a given group of numbers. In the case of a tie, twonumbers are given the same rank. For example, if the set of numbersis 4, 3, 2, 5, the RANK function returns 2, 3, 4, 1. (By default,RANK gives 1 to the largest number.) If the set of numbersis 4, 3, 2, 4, the RANK function returns 1, 3, 4, 1. What do youexpect the sum of the birthday ranks for the 30 people be, if thereare no two people with the same birthday?